Performance analysis of optimal hybrid novel interval type-2 fractional order fuzzy logic controllers for fractional order systems

Abstract

The main objective of this paper is to propose the family of hybrid novel interval type-2 fractional order fuzzy PID (IT2FO-FPID) controllers, which incorporates fractional order integro-differentiator, taking into its consideration the advantages of the interval type-2 fuzzy controllers (IT2FLCs) and fractional order PID (FOPID) controllers. The incorporation of IT2FLCs with FOPID controllers has been investigated in terms of time response measure for unit set-point response and unit load disturbance. The resulting different hybrid IT2FO-FPID controller structures are examined on different fractional order processes followed by robustness analysis. It is observed that incorporation of fractional order integro-differential operators made the proposed control structures less sensitive to the parameters change. For this reason, fractional order integro-differential operators are adopted as design variables along with input/output scaling factors for designing of effective novel controllers. In order to do reasonable comparison, the tuning of the family of hybrid IT2FO-FPID controllers' parameters is done with newly Artificial Bee Colony-Genetic Algorithm (ABC-GA) optimization technique to develop optimal closed loop performance by considering the objective function as weighted sum of control loop error index and control output. The simulation analyses are executed for two different non-integer order plus time delay fractional order process plants (NIOPTD-I and NIOPTD-II). These processes represent a sensible estimation of most process plants and are employed to examine the comparative qualities of the presented hybrid IT2FO-FPID controllers. Further, the performance comparison and the significance of the different proposed hybrid controllers are investigated under unit set-point response, load disturbance rejection, and small control signal or actuators requirement. In order to test the efficacy of proposed controllers, the robustness analysis such as parameter variations is also investigated. Finally, the simulation investigations explicitly suggest that proposed different hybrid IT2FO-FPID control structures can be recommended in terms of better step response, better load disturbance rejection, small control signal response, and parameters variation.